Síðan húsfélagið breytti reglunum lokar þvottahúsið ekki fyrr en klukkan tíu.

Here síðan means since or ever since in a time sense:

Síðan húsfélagið breytti reglunum ...
= Since the homeowners’ association changed the rules ...

That is different from the very common adverb use of síðan, which can mean then, after that, or later.

So in this sentence, síðan is introducing a subordinate clause about a past event that affects the present situation.

This is because Icelandic is a V2 language in main clauses. That means the finite verb usually comes in the second position.

The whole opening clause Síðan húsfélagið breytti reglunum takes the first slot. So the main clause verb has to come next:

Síðan húsfélagið breytti reglunum | lokar | þvottahúsið ekki fyrr en klukkan tíu.

If you said the main clause by itself, without the opening clause, you would normally say:

Þvottahúsið lokar ekki fyrr en klukkan tíu.

So the subject þvottahúsið is still the subject, but it comes after the verb because of normal Icelandic main-clause word order.

Because the sentence describes:

• a past change: húsfélagið breytti reglunum
• a present result: þvottahúsið lokar ekki fyrr en klukkan tíu

In other words:

• the rules were changed earlier
• now, as a result, the laundry room closes later

This is very natural in both Icelandic and English with since:

• Since they changed the rules, it doesn’t close until ten.

So breytti is past because the changing happened before now, while lokar is present because the closing time is the current rule.

Because the verb breyta normally takes the dative case for the thing being changed.

The basic pattern is:

breyta e-u = to change something

So:

• reglur = rules
• reglurnar = the rules
• reglunum = to the rules / the rules in the dative

In this sentence:

húsfélagið breytti reglunum
= the homeowners’ association changed the rules

Even though English just says changed the rules, Icelandic uses the dative after breyta.

Also, -unum here shows:

• plural
• definite
• dative

So reglunum = the rules in dative plural.

Ekki fyrr en means not until.

So:

lokar ekki fyrr en klukkan tíu
= does not close until ten o’clock

Literally, it is something like:

• ekki = not
• fyrr = earlier / sooner
• en = than / before

So the literal sense is not earlier than ten.

This is a very common Icelandic pattern. Compare:

• Ég kem ekki fyrr en á morgun.
  = I’m not coming until tomorrow.

Without ekki, fyrr en can mean before / earlier than in other contexts.

Klukkan tíu is the normal way to say at ten o’clock.

Here klukkan literally means the clock, but in this expression it functions idiomatically to give the time.

So:

• klukkan tíu = at ten o’clock
• klukkan átta = at eight o’clock
• klukkan hálf ellefu = at half past ten / ten thirty

You will also see Hvað er klukkan? meaning What time is it?

So this is just a standard Icelandic time expression, not something you need to translate word-for-word.

That -ið is the definite article attached to the end of the noun.

Icelandic usually puts the at the end of the noun instead of using a separate word like English.

So:

• húsfélag = a homeowners’ association / building association
• húsfélagið = the homeowners’ association

and

• þvottahús = a laundry room
• þvottahúsið = the laundry room

In this sentence, both are definite because the speaker means specific, known things:

• the association for that building
• the laundry room in that building

A húsfélag is not literally just a random house club. It usually refers to the association of residents or owners in a shared building, especially an apartment building.

Depending on context, good English translations could be:

• homeowners’ association
• building association
• residents’ association
• condo association

So in this sentence, it is the body that manages shared rules for the building, such as when common facilities like the laundry room may be used.

Because after the conjunction síðan, the subordinate clause normally has regular subordinate-clause word order, with the subject before the verb:

síðan + subject + verb + object

So:

síðan húsfélagið breytti reglunum

That is the normal pattern here.

The verb-second rule applies to the main clause, which is why you get:

lokar þvottahúsið ...

But inside the subordinate clause, you do not usually move the verb into second position in the same way.

Yes. Þvottahúsið is the subject of lokar.

In Icelandic, the subject does not have to come before the verb in a main clause. Because the sentence begins with another element, the verb comes first in the main clause, and the subject follows it:

... lokar þvottahúsið ekki fyrr en klukkan tíu.

So the structure is essentially:

• first position: Síðan húsfélagið breytti reglunum
• finite verb: lokar
• subject: þvottahúsið

This often feels unusual to English speakers, but it is completely normal Icelandic syntax.